Charge breaking minima in the broken R-parity minimal supersymmetric standard model

We reconsider the possible presence of charge and colour breaking minima in the scalar potential of the minimal supersymmetric standard model (MSSM) and its minimal generalization with R-parity explicitly broken by bilinear terms (RMSSM). First we generalize some results previously derived for the MSSM case. Next we investigate how robust is the MSSM against its RMSSM extension. We examine the constraints on the RMSSM parameter space that follow from the required absence of charge breaking minima in the scalar potential. We point out the possibility of generating non-zero vacuum expectation values for the charged Higgs field which is not present in the MSSM. However, given the smallness of neutrino masses indicated by neutrino oscillation data, we show that the RMSSM represents only a slight perturbation of the MSSM and is thus as safe (or unsafe) as the MSSM itself from unwanted minima in the scalar potential. (author)